The Field-of-View (FOV) of diffractive Exit Pupil Expanders (EPEs) used with Near-to-Eye Displays (NEDs) is typically limited by the refractive index of the available EPE substrate materials. When used with polychromatic light, and neglecting the effect of a display aspect ratio, the horizontal FOV limit can be expressed as (θH is a half angle of the FOV):
                                          sin            ⁢                                                  ⁢                          θ              H                                =                                                                      λ                  min                                ⁢                                  n                  2                                            -                                                λ                  max                                ⁢                                  n                  1                                                                                    n                1                            ⁡                              (                                                      λ                    min                                    +                                      λ                    max                                                  )                                                    ,                                      (          1          )                ,            
wherein n2 is the refractive index of the EPE substrate (or plate), n1 is the refractive index of the surrounding material, and λmin and λmax are minimum and maximum wavelengths of the polychromatic light, respectively. Equation 1 is valid for symmetric exit pupil expansion, i.e., the grating period of the in-coupling diffraction grating is selected so that the horizontal acceptance angles for light guiding are equal for both +1 and −1 diffraction orders.
Equation 1 shows that the FOV of a planar EPE is limited by the refractive index of the materials and the wavelength band of the incident light. For example, using EPE substrate material MGC171 (manufactured by MITSUBISHI GAS CHEMICALS) with the refractive index of n2=1.71 and n1=1 (for air as the surrounding material) we get a theoretical FOV limit of about 40 degrees (full width equal to 2θH) for blue light (λ=465 nm) having 10 nm wavelength bandwidth. When using one EPE plate for blue (465 nm) and green (540 nm) light components and a substrate with n2=1.71, the FOV is reduced to about 29 degrees. If a high index material of n2=2 is used, the FOV limit for the 10 nm wavelength bandwidth and blue light (465 nm) is about 58 degrees, but for the wavelength band covering the visible spectra (λmax=450 nm and λmax=650 nm) the FOV limit is only about 26 degrees.
Looking at the examples presented herein, it is clear that separate EPE plates with refractive index approaching n=2 are required for each RGB (red, green, blue) color to reach the viewing conditions of a typical PC desktops monitor. In practice, such materials are not readily available so other operating principles are needed.